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September, 1991 Monotone Gain, First-Order Autocorrelation and Zero-Crossing Rate
Benjamin Kedem, Ta-Hsin Li
Ann. Statist. 19(3): 1672-1676 (September, 1991). DOI: 10.1214/aos/1176348271


The effect of a linear filter with monotone gain on the first-order autocorrelation of a weakly stationary time series is discussed. When the gain is monotone increasing, the first-order autocorrelation cannot increase. Otherwise, when the gain is monotone decreasing, the correlation cannot decrease. Further, when the gain is strictly monotone, the first-order autocorrelation is unchanged if and only if the process is a pure sinusoid with probability 1. Under the Gaussian assumption, the zero-crossing rate moves oppositely from the first-order autocorrelation.


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Benjamin Kedem. Ta-Hsin Li. "Monotone Gain, First-Order Autocorrelation and Zero-Crossing Rate." Ann. Statist. 19 (3) 1672 - 1676, September, 1991.


Published: September, 1991
First available in Project Euclid: 12 April 2007

zbMATH: 0729.62090
MathSciNet: MR1126347
Digital Object Identifier: 10.1214/aos/1176348271

Primary: 62M10
Secondary: 62M07

Keywords: exponential smoothing , Gaussian , linear filter , sinusoid , spectrum , time series

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.19 • No. 3 • September, 1991
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